Carbon dioxide removal from the atmosphere and storage over long times scales in terrestrial and marine reservoirs is urgently needed to limit global warming and for sustainable management of the global carbon cycle. Ocean alkalinity enhancement by the artificial addition of carbonate minerals to the seafloor has been proposed as a method to sequester atmospheric CO2 and store it in the ocean as dissolved bicarbonate. Here, a reaction-transport model is used to scrutinize the efficacy of calcite addition and dissolution at a well-studied site in the southwestern Baltic Sea – a brackish coastal water body in northern Europe. We find that most calcite is simply buried without dissolution under moderate addition rates. Applying the model to other sites in the Baltic Sea suggests that dissolution rates and efficiencies are higher in areas with low salinity and undersaturated bottom waters. A simple box model predicts a tentative net CO2 uptake rate from the atmosphere of 3.2 megatonnes of carbon dioxide per year for the wider Baltic Sea after continually adding calcite to muddy sediments for 10 years. More robust estimates now require validation by field studies.